Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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puncta quævis EE rectâ lineâ connectantur, iíſque reſpondentia
<
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puncta BB rectâ quoque jungantur; </
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<
s
xml:id
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xml:space
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">quoniam rectæ EB ſibimet
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æquantur (etenim nil aliud ſunt, quam eadem ipſa linea diverſum
<
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<
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xlink:label
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note-0193-01
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note-0193-01a
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xml:space
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">Fig. 5.</
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ſitum obtinens) ac parallelæ ſecundum _hypotbeſin_, erunt rectæ EE,
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BB æquales ac parallelæ. </
s
>
<
s
xml:id
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echoid-s8627
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xml:space
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preserve
">Unde patet curvas EE, BB adæquari ſi-
<
lb
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bimet, & </
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>
<
s
xml:id
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echoid-s8628
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xml:space
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">aſſimilari. </
s
>
<
s
xml:id
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echoid-s8629
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xml:space
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">Adæquari quia ſubtenſæ omnes EE ſubtenſis BB
<
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ſingillatim æquantur; </
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>
<
s
xml:id
="
echoid-s8630
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xml:space
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preserve
">aſſimilari, quia rectæ AB cum ſubtenſis adja-
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centibus reſpectivis EE, & </
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>
<
s
xml:id
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echoid-s8631
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xml:space
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">BB pares angulos conſtituunt, adeóque
<
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rectæ ipſæ EE pares iis, quos rectæ BB; </
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>
<
s
xml:id
="
echoid-s8632
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xml:space
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">ipſæ illæ cum ſeipſis, & </
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>
<
s
xml:id
="
echoid-s8633
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xml:space
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hæ cum ſeipſis (nam in hujuſmodi proportionalitate partium, & </
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>
<
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xml:space
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">an-
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gulorum æqualitate, ſicut alibi fortaſſe luculentiùs & </
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>
<
s
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xml:space
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">fuſiùs diſſere-
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mus, omnis conſiſtit linearum, & </
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>
<
s
xml:id
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echoid-s8636
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xml:space
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">quarumcunque magnitudinum ſimi-
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litudo.) </
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<
s
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xml:space
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">Quod ſi vice commutatâ linea curva BC fiat linea _Genetriæ
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,_
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& </
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<
s
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xml:space
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">recta BA _directrix_, hoc eſt ſi BC per BA ſibi parallela feratur,
<
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<
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xlink:label
="
note-0193-02
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xlink:href
="
note-0193-02a
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">Fig. 6.</
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producetur eadem ipſiſſima parallelogramma Superficies; </
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xml:space
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">& </
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>
<
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xml:id
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echoid-s8640
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xml:space
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">ſingula
<
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rectæ BC puncta, veluti F, rectas lineas ad BA parallelas deſcri-
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bent; </
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>
<
s
xml:id
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xml:space
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">neque non interceptæ FF reſpectivis BB pares erunt; </
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<
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xml:space
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">quod
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& </
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<
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">pari modo ex ſuppoſito perpetuo curvæ BC paralleliſmo facilè con-
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ſectatur. </
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<
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xml:space
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">Sit denique curva quævis (vel è rectis angulos efficientibus
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compoſita, quæ curvæ quoque nomen meritò ferat; </
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<
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xml:space
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">_Archimedes_
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ſaltem è rectis compoſitas lineas, utì figurarum circulis inſcriptarum
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aut adſcriptarum perimetros, {και} {πα}λῶν {γρ}αμμ@ν nomine complecti-
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tur; </
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<
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xml:space
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">ut & </
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<
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">viciſſim curvæ quævis lineæ cenſeri poſſunt è rectis, innu-
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meris quidem illis indefinitè parvis, adjacentibus, & </
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<
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xml:space
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">deinceps ſe-
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cum angulos efficientibus, conſlatæ) ſit, inquam, talis aliqua curva
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BC, in plano quovis conſtituta, tum in alio plano, vel ſuper lineæ
<
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BC planum ut libet elevata, recta AB ſibi continuò feratur parallela,
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modo quo ſemel ac iterum oſtendimus; </
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>
<
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xml:space
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">deſcribetur hujuſmodi motu
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_Superficies cylindrica_ (vel certè _priſmatica, ſi linea directrix è rectis_
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ponatur compoſita) & </
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<
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">_cylindrica_ quidem ſtrictè dicta, ſi _directrix
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_
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_fuerit linea circularis, aut elliptica_; </
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<
s
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">latiore verò ſenſu talis, ſi curva
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fuerit alterius generis ut _parabolica_ puta, vel _hyperbolica_, vel alia
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quæpiam. </
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>
<
s
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xml:space
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">In hoc autem motu lineæ quoque genetricis ſingula puncta
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ſimiles & </
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">æquales deſcribunt curvæ directrici lineas; </
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<
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">æquales
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(ut in mox præcedente diſcurſu) quoniam EB pares ac paral-
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lelæ ſunt; </
s
>
<
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">adeóque EE, BB quoque pares, ac parallelæ
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ſimiles; </
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<
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">*quoniam etiam anguli EEE, angulis BBB æquantur.
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</
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<
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<
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position
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xlink:label
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note-0193-03
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xlink:href
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note-0193-03a
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">10. XI
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. El
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@m.</
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Quinetiam reciprocè deſcribatur eadem Superficies ponendo curvam
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BC perrectam AB parallelωs deportari. </
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<
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">Quomodò ſingula quoque
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curvæ BC puncta rectas parallelas & </
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<
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